Though the Karhunen–Loève expansion has theoretical advantages to other variants to generate a trajectory of a Wiener Process, many users will use different methods because on computers evaluation of trignometric is very expensive in terms of calculation time.

Fourier methods use sine and cosine functions, and are used in calculating option prices, VaR, time series analysis etc. It is an alternative process for doing many things in finance. Some links Fourier Methods in trading on StackExchange and Wiki

When you do Monte Carlo simulation and would like to draw sample from the normal distribution $\mathcal{N}(\mu,\sigma^2)$, you may use
Box-Muller transform and come up with formulas using $\sin$ and $\cos$.

Trigonometric functions are WAVE phenomena. As such, they are best used to model so-called periodic functions, that is, functions with cycles of a fixed period in length. That's why they are good for modelling, seasonal, annual, "blue moon" (once every two and half years), or other functions with set "periods."